Electronic angle generator

ABSTRACT

An electronic angle generator for generating an output voltage proportional to an angle, the tangent of which is a ratio of the two input voltages to the generator, comprising multipliers and function generators utilized for solving the equation X sin theta Y cos theta by closed loop action (implicit computation).

I United States Patent 1151 3,648,041

Beatrice 51 Mar. 7, 1972 [54] ELECTRONIC ANGLE GENERATOR 2,924,7092/1960 Morrill ..235/ 189 X 3,000,565 9/1961 Wilkinson ..235l194 X [72]vemm" 3,407,292 10/1968 c611 ..235/186 [73] Assignee: The United Statesof America 85 3,473,011 10/1969 Schmid. .235/186 X represented y theSeeretan of the y 3,482,086 12/1969 Caswell ..235/186 Filed: J 1,Jordan, J1. Ct PP 45,521 Primary Examiner-Joseph F. Ruggiero Attorney-R.S. Sciascia and J. M. St. Amand [52] US. Cl. ..235/ 186, 235/189,307/229 [51] Int. Cl. ..G06g 7/22 ABSTRACT [58] Field of Search 235/186,189, 197, 194; An electronic an gle generator for generatmg an outputvolt- 328/160 307/229 230 age proportional to an angle, the tangent ofwhich is a ratio of the two input voltages to the generator, comprisingmultipliers [56] References Clted and function generators utilized forso1ving the equation X sin UNITED STATES PATENTS =Ycos 0 by closed loopaction (implicit computation).

2,671,875 3/1954 Urbanik ..235/186 2 Claims, 6 Drawing Figures "fur /24ab I M E a; I

{l -i MULTIPLIER l 2] I F R g 47 J 5111 9 l R H R smcos I an. GENERATORL J 26 1ocose R(TRIM) T I "a. coyzlingga MULTIPLIER I |Y| cos a 1 Y 9 ARELAY" DRIVER i o W 0 TO- A I R .1 i +9o TO 180 (K) I 1 -so T0 -180 AINPUT 1 R L---] COMPARATOR RELAY VQUT FOR DRNWHER Patented March 7, 1972INPUT XOt Sheets-Sheet 2 OUTPUT CONTACTS 0F RELAY m 24 LINVERTINGAMPLIFIER I CONTACTS OF RELAY K3 FIG. 5A

FINTON J. BEATRICE INVENTOR.

ATTORNEY INVERTING AMPLlFlER l J ELECTRONIC ANGLE GENERATOR Theinvention herein described may be manufactured and used by or for theGovernment of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor. Thisdisclosure relates to an analog circuit arrangement which, as shown inFIG. 1, provides an output voltage proportional to an angle, the tangentof which is a ratio of the two input voltages X and Y. Multipliers andfunction generators are utilized for solving the equation X sin =Y cos 6by closed loop action. The problems of ambiguity and instability,typical of conventional implicit computation approaches, are eliminatedby constraining the closed loop which generates the angle 0 always tooperatein the first quadrant where the sine and cosine have oppositeslopes and where feedback is negative. Although the resultant angle isgenerated in the first quadrant, the actual voltage output is madeproportional to 0 over all four quadrants by a linear transformation.When the tangent becomes large, a zenner diode serves as a protectivedevice by limiting the magnitude of the signal.

The normal application of this device is to generate the resultant angleof a vector which is the sum of two orthogonal components (the two inputsignals).

.The conventional electromechanical solution to such a problem is to usea resolver-servomotor approach. Such solution is limited in its speed ofresponse and has an ambiguity in the mechanical angle which satisfiesthe control system.

The usual electronic equivalent of the resolver suffers from theambiguity of solving the equation X sin 0=Y cos 6, and also from loopinstability when the inputs suddenly change polari- The novelty of theinvention disclosed herein is that it forces a nonambiguous solution andoperates stably in all four quadrants.

The scale factor is i volts to represent 1 180. The static accuracy ofthe angle generator holds the error within a band of i 2.5 over its 360range. Insofar as dynamic errors are concerned, the computationalaccuracy and the speed of response of the unit are limited by thecharacteristics of the commercial multipliers'and sine-cosine generatorin the computing loops. Because multipliers are used, dynamicperformance will be degraded by any substantial reduction of the inputsignals. However, for signal frequencies up to 1 Hertz, and inputamplitudes no less than 20 percent of the maximum, the dynamic error isless than 6 percent of full scale, except for a small region near thediscontinuity at i 180.

Dynamic errors are minimal, since the input signals to be applied to theangle generator are the time-averaged outputs from instruments that areessentially narrow band wave analyzers. Therefore, the input componentsto the angle generator are low frequency signals normally scaled by theusual sensitivity adjustments of a frequency analyzer to produce asclose to full range signals as possible.

The technique demonstrated by this invention is an electronic approachto the problem which eliminates the problems of ambiguity andinstability which are typical of conventional implicit computationapproaches.

Other objects and many of the attendant advantages of this inventionwill become readily appreciated as the same becomes better understood byreference to the following detailed description when considered inconnection with the accompanying drawings wherein:

FIG. 1 is a block diagram of an embodiment of the electronic anglegenerator of this invention.

FIG. 2, 3 and 4 illustrate angle generation for various examples.

FIGS. 5A and 58 comprise a circuit schematic diagram showing animplementation of the block diagram of FIG. 1 with detailed subcircuits.

The electronic angle generator described herein generates the angle 0where the following definitions hold:

where C, and Q, are the coincident and quadrature components of thecross-spectral density function G JF Iu'HQJru C and Q are voltagesignals between i 10 volts with time averaging between 0.1 to 10seconds. h

The object is to generate an output voltage which is proportional to theangle whose tangent is the ratio of two input voltages. These voltagesare orthogonal input voltages by definition, as stated above.

An electromechanical solution to the problem is to use aresolverservomotor. approach. However, an electronic approach was takento avoid the problems associated with mechanical devices because offrequency response associated with time lag. The present technique usesmultipliers and function generators to solve the equation X sin 0=Y cos9 by closed loop action (or implicit computation). A new technique hasbeen developed to eliminate the problems of ambiguity and instabilitywhich are typical of the conventional implicit computation approaches.

This scheme restricts computation to first quadrant angles, and useslogical interrelations of the input polarities to determine suitabletransformations which make the output voltage proportional to thedesired angle over all four quadrants.

In the diagrams and circuit descriptions of FIG. 1, consider that C =Xthat Q ,,=Y, and that the angle The general problems of instrumentswhich solve a sinecosine equation by implicit computation are stabilityand ambiguity.

The generation of a voltage proportional to the angle whose tangent is(Y/X) is typically done by forcing the difference (X sin 0-Y cos 6) tobecome arbitrarily small. However, it can be seen that two angles exist,0 and (0+l80"), for which (X sin 0Y cos 0) vanishes for a given X and Y.

In the solid state hardware used to illustrate the present device, thevoltage representing angle does not repeat as it does in a mechanicalresolver. The voltage is a linear function of angle, with -10 voltsrepresenting +l, and +l0 volts representing l80. The sign of the slopesof the sine and cosine are not consistent over the four possiblequadrants. Hence, a fixed choice of polarity around the two loops, whichforces X sin 6=Y cos 6 in one quadrant, can result in positive feedbackand saturation of electronic amplifiers for other polarities of X and Y.

This invention avoids these problems, and is block diagrammed in FIG. 1.The closed loop which generates the angle 0 is constrained to alwaysoperate in the first quadrant, where the sine and cosine have oppositeslopes and the feedback is negative.

Although the computing loop is always solving and therefore generatingthe angle in the first quadrant, the actual output voltage is madeproportional to 0 over all four quadrants by three lineartransformations, as demonstrated in the following examples:

Second Quadrant (see FIG. 2). Consider the case when the inputs are X=',Y=+. Note in FIG.) that 0 =0 =(-l 80+9 computed). Therefore, sincel80=+l0 volts, a positive 10 volt signal is added to the computed 9signal (which is negative), and the result is inverted to produce theoutput which is proportional to actual 0 in the second quadrant. Relaydriver C is used.

Third Quadrant (see FIG. 3). Consider X=--, Y=. Note in FIG. 3 that 0180-6 Thus, if -0, produced by actuating relay driver A," is added to l0volts (a +1 80 equivalent), and the result is inverted using theinverting amplifier 70 and relay driver C," the output is proportionalto actual 0. Relay driver B" provides the -10 volt signal when both Xand Y are negative.

Fourth Quadrant (see FIG. 4). Consider when the inputs are X=+, Y=. Theoutput angle should be in the fourth quadrant. Note in FIG. 4 that it isofthe same magnitude as the computed angle, but of opposite polarity. Alogic arrangement senses the condition of X--+, Y and supplies theinversion of the output signal, by relay driver A."

A zener diode 21 (e.g., 6.8 volts) will be noted across the amplifier inintegrator 22 in the computing loop. This eliminates the possibility ofsaturation for the indeterminite case X=0, Y=0. Multipliers 24 and 26used have the nonideal characteristic of producing some low output whenone input is zero and the other input is a large voltage. Regardless ofthe relative polarity of the net signal to integrator 22, the zenerdiode 21, by both zener breakdown and normal diode action, limits thevoltage output during the indeterminate case, and the recovery is rapidfor any succeeding nonzero input to either X or Y.

Hg. is a circuit diagram which implements the block diagram of FIG. 1.The circuit shown uses relays and is limited in frequency response dueto the nature of the particular electronic multipliers and functiongenerators involved. The technique, however, is not limited 'to suchswitching means and multipliers. Thus, it has no significant limitationon potential frequency response.

The two input voltages, marked X and Yin FIGS. 1 and 5, are directvoltages (i.e.not carrier signals) with magnitudes of between 1 0 voltsand volts. The circuit output voltage is proportional to the angle whosetangent is the ratio of input voltages (1 divided by X). The scalefactor of the output is linear, with minus 10 volts equaling plus 180,and plus 10 volts equaling minus 180.

FIG. 5 has dashed lines defining groups of components which performspecific functions. Several of these are repetitive, and so in thefunctional description each repetitive subcircuit will be examined downto the component level only once. In general, the subcircuits of FIG. 5correspond to the functional boxes shown on FIG. 1.

The input signal X branches out into three paths: it goes directly tothe normally closed contact 31 operated by relay K-1 of relay driver C;"it goes through a unity gain inverting amplifier 32 and appears at thenormally open contact 33 of relay K-l; it goes to a comparator circuitwhich energizes relay driver circuit C" when X goes negative. One of thetwo switching functions carried out by relay driver C is to energizerelay K-l.

It is apparent then that the signal on the swinger of relay K- 1. whichbecomes the a input to Multiplier 24, is a positive voltage equal to themagnitude of X, for X either positive or negative.

Let us consider the circuit details of the three subcircuits mentioned.Resistors R1 and R2, each 100 K ohms, set the unity gain for plug-inoperational amplifier A1. Amplifier Al operates on plus and minus voltpower supplies. Potentiometer R4, 200 K ohms, is a zero output trimresistor for this amplifier. Resistor R3 is the impedance balancingresistor for the noninverting input of amplifier A1. Diode D1 isactually two back-to-back zener diodes (IN3021B, 11 volts +5 percent)which are used to limit any input transients which might significantlyexceed the rated plus to 1 0 volt input range.

Comparator circuit 35 uses amplifier A3. This amplifier is similar toAl, has a differential gain of 100,000 volts/volt, and by having diodeD2 (two back-to-back IN758 zener diodes) as its feedback element, itperforms as a comparator circuit. Resistor R5 feeds in the X signal.Resistor R7 by going to ground provides 0 volts as the reference levelfor the comparator action. Thus for X signal positive the amplifier A3output goes negative until clamped by one of the feedback zener diodesD2 across it. The amplifier output feeds relay driver circuit C." Relaydriver C" is composed basically of transistor Q1 and its associatedcomponents. The common power supply voltages for the instrument are plusand minus 15 volts. The

relays used are 24 volts relays, for example. Thus relay driventransistor Q1 has its emitter biased to -8.2 volts by diode D5 andresistor R9-the diode D5 reduces the l 5 volt supply by 6.8 volts. Thedesired logic decision for X inputs of negative polarity requires theequivalent ofa double pole double throw switch. This is performed byrelays K1 and K2. Diode D3 is a voltage transient suppression diodeacross the inductive load of relay coils K1 and K2. Diode D4 providesreverse voltage protection for the base of transistor Q1. Resistor R6limits the steady state base current to transistor 01 and capacitor C1provides a speed-up action in turning on transistor Q1.

Inverting amplifier 42 with amplifier A2 and associated resistors R15,R16, R17 and R18 operates in a similar manner to inverting amplifier 32described. Comparator 45 with amplifer A4, back-to-back zener diodes D7,and resistors R10, R11 and R12 operates like comparator 35. Relay driverA" with relay coils K3 & K4, diodes D6, D8 & D9, transistor Q2,capacitor C2 and resistors R13 and R14 also operates like relay driverC.

Relay coil K2 operates relay switch swinger arm 36 and relay coil K4operates relay switch swinger arm 46.

The input signal Y branches out into three paths, also: it goes directlyto the normally open contact 41 operated by relay K3 of relay driver A;"it goes through a unity gain inverting amplifier 42 and appears at thenormally closed contact 43 of relay K3; it goes to a comparator circuit45 which energizes relay driven circuit A" when Y goes negative. One ofthe two switching functions carried out by relay driver A is to energizerelay K3.

It is apparent then that the signal on the swinger of relay K3, whichbecomes the (1" input to Multiplier 26, is a negative voltage equal tothe magnitude of Y, for Y either positive or negative.

The implicit computation loop solves the equation X sin 0-) cos 0 0. Itis mechanized by using the two multipliers 24 and 26, a sin-cosgenerator 47 amplifier 50 with capacitor C3 feedback plus associatedresistors in integrator 22, and an inverting amplifier 60 with itsassociated resistors R28, R29, R30, R31, R32, R33 and capacitor C4.

The commercial multipliers 24 and 26 each have two inputs, i.e., 11" andb." Each have an output equal to (aXb)/ 10. The sin-cos generator 47 hasthe characteristic of accepting an input signal with a range from 10 to+10 volts representing the angle 0 varying from plus to minus 180. Thetwo outputs 48 and 49 of sine-cosine generator 47 are scaled to equal 10sin 6 and 10 cos 6 respectively. Since a input to multiplier 24 isalways +X, and the a input to multiplier 26 is always Y, the computingloop will always be stable, i.e., it has no polarity reversals as X and1 go through all permutations of polarity. If the output of multiplier24 is X sin 6, and the output of multiplier 26 is Y cos 0, the sum ofthese two terms will be forced arbitrarily close to zero by thefollowing closed loop action. These two signals are summed in integrator22 by resistor R22 and the combination R23, R24, and R58. The sum isinput to integrating amplifier 50 which functions as an invertingintegrator due to capacitor C3. Since the computing loop is constrainedto operate with one fixed set of signal polarities, the integrator 22output at 23 will also always have one polarity for normal computing.For the indeterminate case of X=0 and Y=0, the imperfections of thecommercial multipliers 24 and 26 may result in some small multiplieroutput signal for zero input. Such residual multiplier signals couldcause computing loop instability for some permutations of polaritybetween them. The zener diode 21 across the integrating capacitor C3eliminates this possibility of saturation for the indeterminate case.The maximum voltage developed by integrator 22 in normal computing isplus 5 volts (less than the zener voltage of 6.8 volts for zener diode21. If residual voltages whose sum is positive are fed to integrator 22,the output level is clamped at about 0.5 volts by zener diode 21providing diode action. Integrator 22 output at 23 drives invertingunity gain amplifier 60, formed by operational amplifier 61 and itsassociated resistors R28, R29, R30,

R31, R32 and R33, which serves a double purpose. It provides the correctsignal polarity to the sin-cos generator for stable computing loopoperation, and is used in the transformations to providetlge correctoutput angle. Since integrator 22 continues to change its output leveluntil the X sin 6 signal equals the Y c'os signal, and the integratoroutput (inverted) drives the sin-cos generator 47, the value at theinput of sincos generator 47 must be proportional to the angle 6, whosetangent is Y over X.

lnverting amplifier 70 with operational amplifier 71 and associatedcircuitry including resistors R35, R36, R37, R38, R39, R40 and R41 issimilar to inverting amplifier 60. Inverting amplifiers 60 and 70 areslightly different from the earlier described inverting amplifiers 32and 42. Operational amplifiers 61 and 71 have a wider frequency responseand faster transient recovery time than amplifiers A1 and A2 used ininverting amplifiers 32 and 42, respectively. The effective inputresistances formed by resistors R28, R29, and potentiometer R30 ininverting amplifier 60 and R35, R37, and potentiometer R34 in invertingamplifier 70, are trimmable for calibration purposes. Small rolloffcapacitors C4 and C5 are used across the feedback resistors R31 and R36,respectively, because of the greater frequency response of amplifiers 61and 71.

This circuit restricts computation to first quadrant angles and useslogical interrelations of the input signal polarities to determinesuitable transformations which make the output voltage proportional tothe desired angle over all four quadrants. See FIG. 1 for the tabulationof which relays are energized for the permutations of input signalpolarities. Details of the reasoning for the transformations used havebeen previously discussed.

In FIG. 5 it can be seen that resistor R19 and diodes D11 and D12 forman AND gate circuit 80 to energize relay driver 8" for the conditionthat both X and Y input signals are negative. If either input ispositive, its respective comparator 35 or 45, i.e., the output ofamplifiers A3 and A4, will be at negative 10 volts, and either diodesD11 or D12 will be conducting. Thus the junction 81 of diodes D11 andD12, resistors R19, and R will be about minus 9.5 volts, keepingrelaydriver 8" off. When both input signals to gate'80 are negative,both amplifiers A3 and A4 outputs will be at plus 10 volts and diodesD11 and D12 will be cutoff, since relay driver 8" will come on as thebase voltage of transistor Q3 becomes more positive than the -8.2 voltsat the Q3 emitter. With relay driver 8" on, the voltage at the junction81 is approximately minus 5 volts. Relay coil K5 of relay driver Boperates to move switch swinger arm 90 from its normal positioncontacting contact 92 to contact 93. Diodes D13, D14 and D16, andtransistor Q3 operate like similar ones in relay drivers A" and C."

The resistance dividers formed by resistors R42 through R49 provide twotrimmable voltages of approximately plus and minus 10 volts. These arerequired for the transformations when the input X is negative. ResistorR50, capacitors C6 and C7, diodes D17 and D18 comprise a filter on theoutput signal which is used to minimize switching transients. Since theoutput is bipolar (plus 10 tominus 10 volts), diode D17 is needed toprotect capacitor C6 for negative output voltages. Similarly, diode D18is needed to protect capacitor C7 for positive output voltages. Bothcapacitors C6 and C7 are polarized solid tantulum capacitors.

What is claimed is:

1. An electronic angle generator system for generating an output voltageproportional to an angle, the tangent of which is a ratio of two inputvoltages to the generator, comprising:

a. a first and a second input channel means to which input voltages Xand Y are applied, respectively, b. a closed computing loop circuitmeans for generating an output voltage proportional'to an angle 0 bysolving the equation the outputs of said first and second input channelmeans being applied to said computing loop circuit means,

0. said first input channel means comprising 1. a first input terminalto which the first input voltage X is applied,

2. said first input terminal being connected to: the normally closedcontact of a first switch means, a first channel voltage inverting meanswhose output is connected to the normally open contact of said firstswitch means, and a first comparator circuit means whose output isconnected to a first switch operating means which operates to switchsaid first switch means from its normally closed contact to its normallyopen contact when the input voltage X to said first channel inputterminal goes negative,

3. a first multiplier means whose first of two inputs is connected tosaid first switch means, the voltage to the first input to said firstmultiplier means being a positive voltage for both positive or negativefirst channel voltage X inputs,

d. said second input channel means comprising 1. A second input terminalto which the second input voltage Y is applied,

2. said second input terminal being connected to: the normally opencontact of a second switch means, a second channel voltage invertingmeans whose output is connected to the normally closed contact of saidsecond switch means, and a second comparator circuit means whose outputis connected to a second switch operating means which operates to switchsaid second switch means from its normally closed contact to itsnormally open contact when the input voltage Y to said second channelinput terminal goes positive,

. a second multiplier means whose first of two inputs is connected tosaid second switch means, the voltage to the first input to said secondmultiplier means being a negative voltage for both positive or negativesecond channel voltage Yinputs,

e. said closed computing loop circuit means solving said equation forthe angle 0 by restricting computation to first quadrant angles andusing logic circuit means for logical interrelations of input polaritiesto determine transformations to make said output voltage proportional tosaid angle over all four quadrants.

2. An electronic angle generator system for generating an output voltageproportional to an angle 6, the tangent of which is a ratio of two inputvoltage X and Y to the generator, comprising:

a. first and second input channel means to which input voltages X and Yare applied, respectively,

b. a closed computing loop circuit means for generating an outputvoltage proportional to an angle 0 by solving the equation Willil byimplicit computation restricting computation to first quadrant anglesusing logic circuit means for logical interrelations of input polaritiesto determine transformations to make said output voltage proportional tosaid angle over all four quadrants,

c. said first input channel means comprising:

1. a first input terminal to which the first input voltage X is applied,

2. said first input terminal being connected to: the normally closedcontact of a-first switchmeans, a first channel voltage inverting meanswhose output is connected to the normally open contact of said firstswitch means, and a first comparator circuit means whose output isconnected to a first switch operating means which operates to switchsaid first switch means from its normally closed contact to its normallyopen contact when the input voltage X to said first channel inputterminal goes negative,

3. a first multiplier means whose first of two inputs is connected tosaid first switch means, the voltage to the first input to said firstmultiplier means being a positive voltage for both positive or negativefirst channel voltage X inputs,

d. said second input channel means comprising:

1. a second input terminal to which the second input voltage Y isapplied,

2. said second input terminal being connected to: the normally opencontact ofa second switch means, a second channel voltage invertingmeans whose output is connected to the normally closed contact of saidsecond switch means, and a second comparator circuit means whose outputis connected to a second switch operating means which operates to switchsaid second switch means from its normally closed contact to itsnormally open contact when the input voltage Y to said second channelinput terminal goes positive,

3. a second multiplier means whose first of two inputs is connected tosaid second switch means, the voltage to the first input to said secondmultiplier means being a negative voltage for both positive or negativesecond channel voltage Y inputs,

c. said closed computing loop circuit means comprising:

1. an integrator means having first and second inputs,

2. a first loop voltage inverting means,

3. a second loop voltage inverting means,

4. an output terminal, and

5. a sine-cosine generator means whose input represents the angle whichcan vary from plus 180 and having first and second outputs representingthe sine and cosine of the angle 0, respectively,

f. the output of said integrator means connected to the input of saidfirst loop voltage inverting means and to the normally closed contactofa third switch means,

. the output of said first loop voltage inverting means being connectedto the normally open contact of said third switch means and to the inputto said sine-cosine generator means, said first loop voltage invertingmeans output providing correct signal polarity to the input of saidsinecosine generator means for stable loop operation,

h. the first output ofsaid sine-cosine generator means being connectedto the second of the two inputs to said first multiplier means, and thesecond output of said sinecosine generator means being connected to thesecond of the two inputs to said second multiplier means,

i. the output ofsaid first multiplier means being directly proportionalto the voltage X sine 6 and connected to the first input to saidintegrator means,

j. the output of said second multiplier means being directlyproportional to the voltage Y cosine 0 and connected to the second inputto said integrator means, the first and second inputs to said integratormeans being summed by said integrator means,

k. said third switch means being connected to the input to said secondloop voltage inverting means and to the normally closed contact of afourth switch means, said third switch means also being operated by saidsecond switch operating means which operates to switch said third switchmeans from its normally closed contact to its normally open contact whenthe input voltage Y to said second channel input terminal goes negative,

1. the output of said second loop voltage inverting means beingconnected to the normally open contact of said fourth switch means toprovide correct angle output at said output terminal when said fourthswitch means is switched from its normally closed contact to itsnormally open contact,

m. said fourth switch means being connected to said output terminal,said fourth switch means also being operated by said first switchoperating means which operates to switch said fourth switch means fromits normally closed contact to its normally open contact when the inputvoltage X to said first channel in ut terminal goes negative, n. theoutput of said irst loop voltage inverting means also providing acorrect angle output at said output terminal when said third switchmeans is switched from its normally closed contact to its normally opencontact,

0. said computing loop circuit solving said equation for the angle 6restricting computation to first quadrant angles using loop circuitrymeans for logical interrelations of input polarities to determinetransformations to make said output voltage proportional to said angleover all four quadrants.

1. An electronic angle generator system for generating an output voltage proportional to an angle, the tangent of which is a ratio of two input voltages to the generator, comprising: a. a first and a second input channel means to which input voltages X and Y are applied, respectively, b. a closed computing loop circuit means for generating an output voltage proportional to an angle theta by solving the equation the outputs of said first and second input channel means being applied to said computing loop circuit means, c. said first input channel means comprising
 1. a first input terminal to which the first input voltage X is applied,
 2. said first input terminal being connected to: the normally closed contact of a first switch means, a first channel voltage inverting means whose output is connected to the normally open contact of said first switch means, and a first comparator circuit means whose output is connected to a first switch operating means which operates to switch said first switch means from its normally closed contact to its normally open contact when the input voltage X to said first channel input terminal goes negative,
 3. a first multiplier means whose first of two inputs is connected to said first switch means, the voltage to the first input to said first multiplier means being a positive voltage for both positive or negative first channel voltagE X inputs, d. said second input channel means comprising
 1. A second input terminal to which the second input voltage Y is applied,
 2. said second input terminal being connected to: the normally open contact of a second switch means, a second channel voltage inverting means whose output is connected to the normally closed contact of said second switch means, and a second comparator circuit means whose output is connected to a second switch operating means which operates to switch said second switch means from its normally closed contact to its normally open contact when the input voltage Y to said second channel input terminal goes positive,
 3. a second multiplier means whose first of two inputs is connected to said second switch means, the voltage to the first input to said second multiplier means being a negative voltage for both positive or negative second channel voltage Y inputs, e. said closed computing loop circuit means solving said equation for the angle theta by restricting computation to first quadrant angles and using logic circuit means for logical interrelations of input polarities to determine transformations to make said output voltage proportional to said angle over all four quadrants.
 2. said first input terminal being connected to: the normally closed contact of a first switch means, a first channel voltage inverting means whose output is connected to the normally open contact of said first switch means, and a first comparator circuit means whose output is connected to a first switch operating means which operates to switch said first switch means from its normally closed contact to its normally open contact when the input voltage X to said first channel input terminal goes negative,
 2. said second input terminal being connected to: the normally open contact of a second switch means, a second channel voltage inverting means whose output is connected to the normally closed contact of said second switch means, and a second comparator circuit means whose output is connected to a second switch operating means which operates to switch said second switch means from its normally closed contact to its normally open contact when the input voltage Y to said second channel input terminal goes positive,
 2. An electronic angle generator system for generating an output voltage proportional to an angle theta , the tangent of which is a ratio of two input voltage X and Y to the generator, comprising: a. first and second input channel means to which input voltages X and Y are applied, respectively, b. a closed computing loop circuit means for generating an output voltage proportional to an angle theta by solving the equation by implicit computation restricting computation to first quadrant angles using logic circuit means for logical interrelations of input polarities to determine transformations to make said output voltage proportional to said angle over all four quadrants, c. said first input channel means comprising:
 2. said first input terminal being connected to: the normally closed contact of a first switch means, a first channel voltage inverting means whose output is connected to the normally open contact of said first switch means, and a first comparator circuit means whose output is connected to a first switch operating means which operates to switch said first switch means from its normally closed contact to its normally open contact when the input voltage X to said first channel input terminal goes negative,
 2. a first loop voltage inverting means,
 2. said second input terminal being connected to: the normally open contact of a second switch means, a second channel voltage inverting means whose output is connected to the normally closed contact of said second switch means, and a second comparator circuit means whose output is connected to a second switch operating means which operates to switch said second switch means from its normally closed contact to its normally open contact when the input voltage Y to said second channel input terminal goes positive,
 3. a second multiplier means whose first of two inputs is connected to said second switch means, the voltage to the first input to said second multiplier means being a negative voltage for both positive or negative second channel voltage Y inputs, e. said closed computing loop circuit means comprising:
 3. a second loop voltage inverting means,
 3. a first multiplier means whose first of two inputs is connected to said first switch means, the voltage to the first input to said first multiplier means being a positive voltage for both positive or negative first channel voltage X inputs, d. said second input channel means comprising:
 3. a second multiplier means whose first of two inputs is connected to said second switch means, the voltage to the first input to said second multiplier means being a negative voltage for both positive or negative second channel voltage Y inputs, e. said closed computing loop circuit means solving said equation for the angle theta by restricting computation to first quadrant angles and using logic circuit means for logical interrelations of input polarities to determine transformations to make said output voltage proportional to said angle over all four quadrants.
 3. a first multiplier means whose first of two inputs is connected to said first switch means, the voltage to the first input to said first multiplier means being a positive voltage for both positive or negative first channel voltagE X inputs, d. said second input channel means comprising
 4. an output terminal, and
 5. a sine-cosine generator means whose input represents the angle theta which can vary from plus 180* and having first and second outputs representing the sine and cosine of the angle theta , respectively, f. the output of said integrator means connected to the input of said first loop voltage inverting means and to the normally closed contact of a third switch means, g. the output of said first loop voltage inverting means being connected to the normally open contact of said third switch means and to the input to said sine-cosine generator means, said first loop voltage inverting means output providing correct signal polarity to the input of said sine-cosine generator means for stable loop operation, h. the first output of said sine-cosine generator means being connected to the second of the two inputs to said first multiplier means, and the second output of said sine-cosine generator means being connected to the second of the two inputs to said second multiplier means, i. the output of said first multiplier means being directly proportional to the voltage X sine theta and connected to the first input to said integrator means, j. the output of said second multiplier means being directly proportional to the voltage -Y cosine theta and connected to the second input to said integrator means, the first and second inputs to said integrator means being summed by said integrator means, k. said third switch means being connected to the input to said second loop voltage inverting means and to the normally closed contact of a fourth switch means, said third switch means also being operated by said second switch operating means which operates to switch said third switch means from its normally closed contact to its normally open contact when the input voltage Y to said second channel input terminal goes negative, 